Robust Preconditioning: Optimal control of the convection-diffusion equation with limited observation

MSc Jarle Sogn

Oct. 6, 2020, 3:30 p.m. S2 054

We consider an optimization problem with a Convection--Diffusion--Reaction equation as constraint.
A Schur complement preconditioner is proposed and we show that the problem is well-posed.
The proposed preconditioner is robust with respect to all the problem parameters and the condition number of the preconditioned problem bounded by 4.05.
We provide conditions for inf-sup stable discretizations and show one such discretization for box domains with constant convection.
For this discretization, we derive error estimates. Finally, we provide numerical example highlighting the method.